Some results on (a: b)-choosability

Shai Gutner, Michael Tarsi

Research output: Contribution to journalArticlepeer-review


A solution to a problem of Erdo{double acute}s, Rubin and Taylor is obtained by showing that if a graph G is (a : b)-choosable, and c / d > a / b, then G is not necessarily (c : d)-choosable. Applying probabilistic methods, an upper bound for the kth choice number of a graph is given. We also prove that a directed graph with maximum outdegree d and no odd directed cycle is (k (d + 1) : k)-choosable for every k ≥ 1. Other results presented in this article are related to the strong choice number of graphs (a generalization of the strong chromatic number). We conclude with complexity analysis of some decision problems related to graph choosability.

Original languageEnglish
Pages (from-to)2260-2270
Number of pages11
JournalDiscrete Mathematics
Issue number8
StatePublished - 28 Apr 2009


  • (a : b)-choosability
  • Complexity of graph choosability
  • List-chromatic conjecture
  • Probabilistic methods
  • Strong chromatic number
  • kth choice number of a graph


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